It feels as though the cron task locking is going wrong, as you should be able to run cron every minute without the problem you are seeing (and this is how it is working on other sites I've investigated).
I don't know what database system you're using, or if you have a multi-server cluster running your site, but you may be able to try out different settings for $CFG->lock_factory in your main config.php to see if one of the other alternatives works better (something to research carefully before you start messing around with it).
https://github.com/moodle/moodle/blob/master/config-dist.php#L568
I don't know what database system you're using, or if you have a multi-server cluster running your site, but you may be able to try out different settings for $CFG->lock_factory in your main config.php to see if one of the other alternatives works better (something to research carefully before you start messing around with it).
https://github.com/moodle/moodle/blob/master/config-dist.php#L568